Prove that the quadrilateral ABCD whose vertices are (8, 3), (7, 8), (

1.	Prove that the quadrilateral ABCD whose vertices are (8, 3), (7, 8), (2, 7) and (3, 2) taken in order is a square. Also, find its area. Plz friends answer fast I WILL MARK AS BRAINLIEST
Answer» ong>Given, The coordinates of the four vertices of the quadrilateral are (8,3) , (7,8) , (2,7) and (3,2). To find, The quadrilateral is a square and the AREA of the square. Solution, We can prove the quadrilateral is a square by showing that the four SIDES are equal and one angle is 90°. Length of AB = ✓(8-7)²+(3-8)² = ✓1+25 = ✓26 units Length of BC = ✓(7-2)²+(8-7)² = ✓25+1 = ✓26 units Length of CD = ✓(2-3)²+(7-2)² = ✓1+25 = ✓26 units Length of AD = ✓(3-8)²+(2-3)² = ✓25+1 = ✓26 units Now, if the angle ABC is 90°, then it's components will satisfy the Pythagoras theorem. Length of AC diagonal = ✓(8-2)²+(3-7)² = ✓36+16 = ✓52 units (AC)² = (✓52)² = 52 units Now, (AB)²+(BC)² = (✓26)²+(✓26)² = 52 units So, (AC)² = (AB)²+(BC)² We can SAY that, the angle ABC is 90° And, ABCD is a square. Area of ABCD = (✓26)² = 26 unit² Hence, it is PROVED that ABCD is a square and it's area is 26 unit².

Prove that the quadrilateral ABCD whose vertices are (8, 3), (7, 8), (2, 7) and (3, 2) taken in order is a square. Also, find its area. Plz friends answer fast I WILL MARK AS BRAINLIEST

Answer»

ong>Given,

The coordinates of the four vertices of the quadrilateral are (8,3) , (7,8) , (2,7) and (3,2).

To find,

The quadrilateral is a square and the AREA of the square.

Solution,

We can prove the quadrilateral is a square by showing that the four SIDES are equal and one angle is 90°.

Length of AB = ✓(8-7)²+(3-8)² = ✓1+25 = ✓26 units

Length of BC = ✓(7-2)²+(8-7)² = ✓25+1 = ✓26 units

Length of CD = ✓(2-3)²+(7-2)² = ✓1+25 = ✓26 units

Length of AD = ✓(3-8)²+(2-3)² = ✓25+1 = ✓26 units

Now, if the angle ABC is 90°, then it's components will satisfy the Pythagoras theorem.

Length of AC diagonal = ✓(8-2)²+(3-7)² = ✓36+16 = ✓52 units

(AC)² = (✓52)² = 52 units

Now,

(AB)²+(BC)² = (✓26)²+(✓26)² = 52 units

So,

(AC)² = (AB)²+(BC)²

We can SAY that, the angle ABC is 90°

And, ABCD is a square.

Area of ABCD = (✓26)² = 26 unit²

Hence, it is PROVED that ABCD is a square and it's area is 26 unit².